The light intensity (Y) produced by a Cathode Ray Tube (CRT) monitor is controlled by the voltage input. A transfer function of the CRT monitor is the light intensity (Y) produced by a Cathode Ray Tube (CRT) monitor varying with respect to the voltage input (V). Typically, the transfer function of a CRT monitor is in the form of a power law (for example, Y=aVγ, where a is a constant). The exponent of the power law, γ, is frequently referred to as the gamma of the CRT monitor. The theoretical value of the gamma of a CRT monitor, dictated by the physics of the electron gun of a CRT monitor, is around 2.5. Thus, a linear variation in voltage input (V) results in a nonlinear variation in light intensity (Y) in the form of a power law. On a color CRT monitor, red, green and blue phosphors are driven independently by corresponding signals. The light intensities produced by the phosphors in response to the corresponding signals follow the same power law.
A computer system may have a nonlinear built-in unit that is closely associated with the CRT monitor (e.g., a graphics controller, or circuitry in the monitor) such that the light intensity produced by the CRT monitor varies with respect to the input digital signal to the display device in the form of a power law controlled by a gamma different from the gamma for the CRT monitor. For example, a typical Apple Macintosh display has a gamma close to 1.8; and a typical PC display has a gamma close to 2.2. Thus, different display devices have different nonlinearities (different gammas) in their transfer functions.
In this description, the transfer function per channel of the uncompensated device is referred as native transfer function. The native transfer function is assumed to be different from the desired device transfer function, that is referred as target transfer function. The process of pre-compensating for the nonlinearity in the native transfer function of a display device to a target transfer function is known as gamma correction. With a gamma correction, an input digital signal is mapped by a correction function to a corrected signal such that, when the corrected signal is applied to the display system, the light intensity produced by the display device varies with respect to the input digital signal in the form of a power law with a target gamma. With the gamma correction, the display system behaves as if the transfer function of the system has the target gamma. In case of multiple color channel devices, gamma correction is a unidimensional correction applied per channel. This means that the input signal from one channel is mapped into an output signal for that channel. The correction function is computed based on the native transfer function of the device measured as a correlate of the intensity of light (luminance or density) with the input signal. The intensity of light is used only, neglecting the chrominance information.
In general, a gamma correction maps input signals representing the intensity of a light to corrected signals using a nonlinear function. Gamma corrections may be applied to signals for display devices, as well as signals to or from other color related devices, such as scanners, printers, video cameras, and others. Thus, a gamma correction changes or encodes the nonlinearity in signal intensity in each of the color signals using a nonlinear unidimensional mapping function for each channel.
On a color CRT display, since the native transfer functions of the three different color components (e.g., red, green and blue in a RGB color space) of a CRT display follow the same power law, a single parameter gamma correction in the form of a power law can be used to map the input signals of each color channel to the corrected signals.
However, some display devices, such as twisted nematic Thin-Film Transistor Liquid-Crystal Displays (TFT LCD), have a similar transfer functions for different color components. Thus, different unidimensional correction functions are required to correct the asimilar transfer functions to similar target transfer functions. A conventional gamma correction applies different unidimensional correction functions to the input signals for different color components; and the different unidimensional correction functions are derived independently from each other from the native transfer functions and the target transfer functions. Not only that, but the TFT LCD devices show a different native transfer function than a power law requiring table based gamma compensation. Typically, these unidimensional correction functions are in the form of unidimensional look-up tables that map the input digital signals to the corrected signals. Because of the asymmetry of the RGB channels, the gray balance of those devices is poor. Due to the human visual system sensitivity to color differences especially for neutral colors (grays), small asymmetries in the color balance associated with gray color rendition, is usually perceived as a hue shift over the grays. This hue shift is known as color cast and is visible in the form of bluish, greenish or reddish grays depending on the color asymmetry on that device. Additionally, in many cases, TFTLCD devices may show a variation of the chromaticity of the primary colors with the input signal. In the case of gamma correction per channel based on light intensity only per channel, when all compensated channels are combined to represent a gray, the combined compensations may cause a noticeable hue shift for different input signal levels.